High-dimensional integration: the quasi-Monte Carlo way
This paper is a contemporary review of QMC ('quasi-Monte Carlo') methods, that is, equal-
weight rules for the approximate evaluation of high-dimensional integrals over the unit cube …
weight rules for the approximate evaluation of high-dimensional integrals over the unit cube …
[BOOK][B] Monte carlo and quasi-monte carlo sampling
C Lemieux - 2009 - Springer
Quasi–Monte Carlo methods have become an increasingly popular alternative to Monte
Carlo methods over the last two decades. Their successful implementation on practical …
Carlo methods over the last two decades. Their successful implementation on practical …
[BOOK][B] Tractability of Multivariate Problems: Standard information for functionals
E Novak, H Woźniakowski - 2008 - books.google.com
This is the second volume of a three-volume set comprising a comprehensive study of the
tractability of multivariate problems. The second volume deals with algorithms using …
tractability of multivariate problems. The second volume deals with algorithms using …
Application of quasi-Monte Carlo methods to elliptic PDEs with random diffusion coefficients: a survey of analysis and implementation
This article provides a survey of recent research efforts on the application of quasi-Monte
Carlo (QMC) methods to elliptic partial differential equations (PDEs) with random diffusion …
Carlo (QMC) methods to elliptic partial differential equations (PDEs) with random diffusion …
Walsh spaces containing smooth functions and quasi–Monte Carlo rules of arbitrary high order
J Dick - SIAM Journal on Numerical Analysis, 2008 - SIAM
We define a Walsh space which contains all functions whose partial mixed derivatives up to
order δ≥1 exist and have finite variation. In particular, for a suitable choice of parameters …
order δ≥1 exist and have finite variation. In particular, for a suitable choice of parameters …
A tool for custom construction of QMC and RQMC point sets
Abstract We present LatNet Builder, a software tool to find good parameters for lattice rules,
polynomial lattice rules, and digital nets in base 2, for quasi-Monte Carlo (QMC) and …
polynomial lattice rules, and digital nets in base 2, for quasi-Monte Carlo (QMC) and …
Discrepancy theory and quasi-Monte Carlo integration
J Dick, F Pillichshammer - A panorama of discrepancy theory, 2014 - Springer
In this chapter we show the deep connections between discrepancy theory on the one hand
and quasi-Monte Carlo integration on the other. Discrepancy theory was established as an …
and quasi-Monte Carlo integration on the other. Discrepancy theory was established as an …
Explicit constructions of quasi-Monte Carlo rules for the numerical integration of high-dimensional periodic functions
J Dick - SIAM Journal on Numerical Analysis, 2007 - SIAM
In this paper, we give explicit constructions of point sets in the s-dimensional unit cube
yielding quasi-Monte Carlo algorithms which achieve the optimal rate of convergence of the …
yielding quasi-Monte Carlo algorithms which achieve the optimal rate of convergence of the …
Component-by-component construction of randomized rank-1 lattice rules achieving almost the optimal randomized error rate
We study a randomized quadrature algorithm to approximate the integral of periodic
functions defined over the high-dimensional unit cube. Recent work by Kritzer, Kuo, Nuyens …
functions defined over the high-dimensional unit cube. Recent work by Kritzer, Kuo, Nuyens …
Fast component-by-component construction, a reprise for different kernels
Summary In [16](Nuyens and Cools) it was shown that it is possible to generate rank-1
lattice rules with n points, n being prime, in a fast way. The construction cost in shift-invariant …
lattice rules with n points, n being prime, in a fast way. The construction cost in shift-invariant …